Practice Set - Week 2

Author

SOPHAS

Published

24-Apr-2025

Q1. The pass result of 50 students who took a class test is given below:

Marks No of students
40 8
50 10
60 9
70 6
80 4
90 3

If the mean marks for all the students were 51.6, find out the mean marks of the students who failed.

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Q2. The average dividend declared by a group of 10 pharma companies was 18 per cent. Later on, it was discovered that one correct figure, 12, was misread as 22. Find the correct average dividend.

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Q5. Average marks section A of class 9 is 70 and average marks of section B of class 9 is 80. Find the average marks of class 9, assuming:

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Q6. \(x_1\), \(x_2\), \(…\), \(x_n\) are \(n\) values. We are to calculate sum of squared deviation around a number \(a\) as follows:

\[ SSD = (x_1 - a)^2 + (x_2 - a)^2 + … + (x_n - a)^2 \]

Show that \(SSD\) is minimum when a is the mean of the given values.

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Q7. Median is not affective by extreme values. Give examples in support of your answer.

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Q8. Somnath does data analysis for a company. The data on tea consumption (in grams) for the company are as follows:

14.77 16.11 16.11 15.05 15.99 14.91 15.27 16.01 15.75 14.89 16.05 15.22 16.02 15.24 16.11 15.02

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Q9. Following are the responses from 55 employees to the question about how much time they travel to reach the office (in mins).

055 060 080 080 080 085 085 085 090 090 090

090 092 094 095 095 095 095 100 100 100 100

100 100 105 105 105 105 109 110 110 110 110

112 115 115 115 115 115 120 120 120 120 120

124 125 125 125 130 130 140 140 140 145 150

Calculate the range and interquartile range and interpret your result.

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Q10. An agriculture farm sells grab bags of flower bulbs. The bags are sold by weight; thus the number of bulbs in each bag can vary depending on the varieties included.

Below are the number of bulbs in each of the 20 bags sampled:

21 33 37 56 47 25 33 32 47 34

36 23 26 33 37 26 37 37 43 45

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Q11. The wholesale prices of a commodity for a week are as follows:

Days: 1 2 3 4 5 6 7

Commodity price/kg: 240 260 270 245 255 286 264

Calculate the variance and standard deviation.

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Q12. (Continue from Q11) Suppose for next week, price/kg is just 10 more than previous week.

Calculate the variance and standard deviation. What is your conclusion?

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